Volatility

Volatility is a numerical estimate of how widely an asset's price swings over a chosen period. It describes not the direction of the move but its amplitude. Two instruments can deliver the same result over a year, yet one gets there smoothly while the other lurches up and down, and it is the second that is more volatile. Almost all applied portfolio mathematics rests on this quantity: beta, the Sharpe ratio and value at risk are all derived from it.

What the resulting value depends on

There is no single "correct" figure for volatility, only the outcome of three choices. The first is the observation interval. Minute, daily and monthly returns on the same security give different pictures, because intraday noise is smoothed out over a longer interval. The second is the window length. A short window reacts to the most recent days and is itself jumpy, while a long one averages calm and turbulent periods into a single number. The third is the source. An estimate based on past prices is historical volatility; an estimate extracted from option prices shows the swings the market expects ahead, and the sensitivity of the premium to it is measured by option vega.

Scaling a short interval up to an annual figure relies on the assumption that returns are independent of one another. In reality they cluster: turbulent days follow turbulent days, and calm days follow calm ones. As a result, a measure taken during a lull systematically underestimates the size of the next storm.

An example using the site's data

The one-year chart shows the same thing the formula calculates, but without the averaging: you can see where the price moved in a narrow range and where the amplitude widened:

Where the measure lets you down

The main mistake is to treat volatility as a synonym for risk. It measures fluctuations, not the probability of losing your investment for good: a security facing delisting or an issuer on the eve of default can trade quietly for as long as the market is unaware of the problem. The opposite trap is a thinly traded instrument. When there are few trades, the price stays put simply because nobody is trading, and poor liquidity masquerades as low volatility; the true range of swings reveals itself the moment you try to exit. Finally, the volatility of an individual security says little about a portfolio: the overall dispersion depends on how the securities move relative to one another, that is, on their correlation.